Question

The pressure drop by a fan is directly proportional to the ............. of the fan speed.

• A. Cube
• B. Cube root
• C. Square root
• D. Square

Hint:

Remember the progression of Fan Affinity Laws:
- Flow rate \(\rightarrow\) linear (\(N^1\))
- Pressure \(\rightarrow\) quadratic (\(N^2\))
- Power \(\rightarrow\) cubic (\(N^3\))

Answer 1

The Correct Option is D

Step 1: Understanding the Concept:
Fan affinity laws describe the relationships between fan performance variables (such as discharge volume flow rate, pressure drop, and power consumption) and the rotational speed of the fan impeller.
Key Formula or Approach:
According to the fan affinity laws, if the impeller diameter is kept constant:
- Flow rate (\(Q\)) is directly proportional to the fan speed (\(N\)):
\[ Q \propto N^1 \]
- Pressure drop or head (\(\Delta P\)) is directly proportional to the square of the fan speed (\(N\)):
\[ \Delta P \propto N^2 \]
- Power consumption (\(P\)) is directly proportional to the cube of the fan speed (\(N\)):
\[ P \propto N^3 \]

Step 2: Detailed Explanation:
Let the initial speed of the fan be \(N_1\) and the initial pressure drop be \(\Delta P_1\).
If the speed changes to \(N_2\), the new pressure drop \(\Delta P_2\) is given by:
\[ \frac{\Delta P_2}{\Delta P_1} = \left(\frac{N_2}{N_1}\right)^2 \]
This quadratic relationship indicates that the pressure drop across the fan depends directly on the square of the rotational speed of the fan blades.

Step 3: Final Answer:
The pressure drop is directly proportional to the square of the fan speed.